Why is the "replacement fertility rate" not exactly 2?

[swampwiz]

I've never understood this, and although I've had commenters give *qualitative* reasons, I'd like to get the raw mathematics on exactly this is so.

 

[jim mcnamara]

Do you have a citation so we can figure out what is going on? Thanks.

i.e., https://www.quora.com/Why-is-the-replacement-fertility-rate-in-developed-countries-2-1-and-not-2-0
is this what you are referring to? ... for example.

 

[Buzz Bloom]

Hi swampwiz:

Noun

1.

fertility rate - the ratio of live births in an area to the population of that area; expressed per 1000 population per year

https://www.thefreedictionary.com/FERTILITY+RATE

Not all live birth babies survive to have children of their own.

Regards,
Buzz

 

[jim mcnamara]

Type I survivorship curve is what @Buzz Bloom is referring to.
https://en.wikipedia.org/wiki/Survivorship_curve.

 

[jim mcnamara]

Unless we know what you are talking about this topic has multiple answers. We need an explicit definition.

The reply above assumed humans. Other mammals can be similar.
Humans:
Which have 105:100 male female birth ratios and differential suvivorship which is gender dependent.
This is not true for fish, for example. Or Elm trees.

 

[Buzz Bloom]

Hi swampwiz :

I found another Wikipedia definition that perhaps presents a clearer explanation.

https://en.wikipedia.org/wiki/Total_fertility_rate​

• 2.3 Replacement rates

Replacement fertility is the total fertility rate at which women give birth to enough babies to sustain population levels. According to the UN Population Division, a total fertility rate (TFR) of about 2.1 children per woman is called replacement-level fertility. If replacement level fertility is sustained over a sufficiently long period, each generation will exactly replace itself. The replacement level of TFR is dependent also on maternal mortality and child mortality, and, as such, it is higher in underdeveloped countries. The replacement fertility rate is indeed only slightly above 2.0 births per woman for most industrialized countries (2.075 in the UK, for example), but ranges from 2.5 to 3.3 in developing countries because of higher mortality rates, especially child mortality.​

Regards,
Buzz

 

[Dale]

but ranges from 2.5 to 3.3 in developing countries because of higher mortality rates, especially child mortality

Oh, that is sad. It means roughly that out of every 3 kids one will die before adulthood

 

[swampwiz]

It would seem that the pre-motherhood mortality would be included in the fertility rate.

Perhaps my understanding of "fertility rate" is wrong, but I would imagine that it means "how many children does every woman eventually have". So a woman that dies before being of motherhood age would count the same as a childless woman that lives to a ripe old age.

I could see how a male/female birth ratio not being 1 could skew this. My understanding is that there are typically 1.06 males per females on average, so that would mean that 2.06 total children would produce a single female, and so the fertility rate would need to be ( 1 + X ) where X is this male-to-female ratio.

 

[Dale]

Perhaps my understanding of "fertility rate" is wrong, but I would imagine that it means "how many children does every woman eventually have". So a woman that dies before being of motherhood age would count the same as a childless woman that lives to a ripe old age.

It assumes that the woman survives until the end of her reproductive life.

 

[jim mcnamara]

Consider the math behind Cohort Life Tables (How you generate survivorship)
http://www.tiem.utk.edu/~gross/bioed/bealsmodules/lifetables.html

The link is for a plant species. The same arithmetic operations are done for every species for which this data is known.

Excel with human data - link: Notice the first few years (<5 y/a) of increase mortality.


The term you are defining above is fecundity, I think. Try that in a search.

Anyway, the number 2.1 is somewhat arbitrary and variable across populations. Which is why I asked for a citation. As the number goes above 2.1, it requires additional pregnancies.